Question

[Electro Wizard]

CMR:

a)1/1.2+1/2.3+1/3.4+1/4.5+...+1/49.50<1

b)9/20<1/2²+1/3²+1/4²+1/5²+...+1/100²<1

Answer 1

[Phùng Minh Quân]

\(a)\) Đặt \(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\) ta có : 

\(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

\(A=1-\frac{1}{100}=\frac{99}{100}< 1\)

Vậy \(A< 1\)

Chúc bạn học tốt ~